Nine, like War, was a battle scarred Warrior that didn't suffer fools lightly, but masked his pain with a cheery/jovial demeanour.

Ten, like Eight, was a youthful human-like Adventurer, filled with the enthusiasm to see new places and meet new people.

Eleven, like Seven, was silly and childish on the outside, but had a much darker and more manipulative side underneath.

Twelve, like Six, is a bit pompous and lacking in people skills; truthful and pragmatic to the point of rudeness, but still kind and caring on the inside.

It's probably just coincidence. Only natural that so many versions of the same character would under and over-emphasize similar attributes to keep the character interesting, but it does seem to line up quite well.

So if the pattern holds true, our next Doctor will be a bit softer and gentlemanly like Davison.

To me personally, 12 reminds me more of the First, the Sixth and the Seventh Doctors; the initial indignance and arrogance of the First, the brashness of the Sixth and the darkness of the Seventh.

Considering the idea of the War Doctor wasn't really thought of for a number of years after the 9th Doctor this is phenominally unlikely

Plus, the fact that the only reason the war doctor is so like Eccleston's doctor is probably because he was a last minute idea when they couldn't actually get Eccleston to be in the 50th, so, Moffat, having envisioned it as 9, 10, and 11 in his head still basically ended up writing the war doctor very much like the 9th even if he didn't realise how much so.

Had War not existed then Nine would be the eye of the storm.
The mirror image remains intact.
Come on guys, that's Improbable Conspiracy Theory 101.

Gosh! In the ten years since DW came back, I've never thought of it like that. Never even crossed my mind.

Doctor personality maths...

4+6=9
5+8=10
2+7=11
1+3=12

That seems pretty sound too.

That's good - I cannot fault that at all!